Asked by coni
Find the equation of a hyperbola which is generated by a point that moves so that the difference of its distance from the points (-4,1) and (2,1) is 4.
Answers
Answered by
Reiny
let (x,y) be any pt on the hyperbola
from your condition
√[(y-1)^2+(x+4)^2] - √[(y-1)^2+(x-2)^2] = 4
I moved the second radical to the right side, squared each side and simplified to get
3x-1 = √[(y-1)^2+(x-2)^2]
squaring again and simplifying I get
5x^2 + 10x - 4y^2 + 8y = 19
after completing the square I ended up with the standard form of
(x+1)^2/4 - (y-1)^2/5 = 1
from your condition
√[(y-1)^2+(x+4)^2] - √[(y-1)^2+(x-2)^2] = 4
I moved the second radical to the right side, squared each side and simplified to get
3x-1 = √[(y-1)^2+(x-2)^2]
squaring again and simplifying I get
5x^2 + 10x - 4y^2 + 8y = 19
after completing the square I ended up with the standard form of
(x+1)^2/4 - (y-1)^2/5 = 1
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